An automobile approaching a traffic signal comes to a complete stop.
what is the direction of the force acting on the automobile with respect
to the motion of the automobile? explain your answer.

With respect to the car's motion, the direction of the force acting on it as it approaches the red light must be opposite to the direction it's moving.

Since you're doing this question for Physics class, the best way to explain it is using one of Newton's laws of motion, especially the 2nd law:

Newton's #2: Net force = (mass) x (acceleration)

This is a vector equation ... that's why I underlined the vectors.  The net force and the acceleration it produces are both vectors, in the same direction.  (Makes sense.  That's why we push things in the direction we want them to go !)

==> If you want to stop a moving car, you have to decrease its speed forward.

==> That's the same thing as increasing its speed backward.

==> An easier way to say that is:  Accelerate it in the direction opposite to the way it's moving.

==> So you need to apply a net force (push the car) in the direction opposite to the way it's moving.

need to see circuit to get time constant